Which order gives the combatant commander all essential execution planning information when acceleration is required?

The Planning Order is the correct choice because it is specifically designed to provide the combatant commander with detailed information necessary for execution planning, especially in situations where acceleration is needed. This order outlines the necessary steps to prepare for an operation, ensuring that all essential components are adequately addressed.

In circumstances that require rapid action, the Planning Order allows commanders to identify task objectives, allocate resources, and assess operational risks while still allowing for flexibility in execution. It serves to coordinate the various elements of operations, which is vital in time-sensitive situations.

The other options serve different purposes: the Execution Order typically provides directives for carrying out an operation once planning is complete; the Alert Order activates forces and units to be ready for possible deployment, but does not provide detailed planning information; the Mission Order outlines the specific tasks to accomplish during an operation but may not necessarily convey comprehensive planning details required for execution under accelerated timelines.